Theresa May’s plan to write the Brexit divorce date into law has been dismissed as a “gimmick”.
The Prime Minister’s proposal also led to fresh warnings it could provoke a Tory revolt as MPs gathered to debate the legislation.
Mrs May wants 11pm on March 29, 2019 to be enshrined in law as the point at which the UK separates from the European Union.
But the move was condemned by Labour, with shadow Brexit Secretary Kier Starmer branding it a "desperate gimmick" in an effort to keep her party's Eurosceptics in line.
"The Government's amendments to their own Bill would stand in the way of an orderly transition and increase the chance of Britain crashing out of Europe without an agreement," Mr Starmer added.
"Theresa May should stop pandering to the 'no deal' enthusiasts in her own party and withdraw these amendments. If not, Labour will vote against them to support our own amendments and guarantee a transition that protects jobs and living standards."
Several Tory MPs joined the Labour party in demanding Mrs May withdraws the key legislation.
Former chancellor Ken Clarke said the move was "silly”, while Dominic Grieve said it would "fetter" ministers' hands if talks dragged on to the last minute.
Mr Clarke, a staunch Remainer and Conservative MP, said the amendment on the date was "not just ridiculous and unnecessary - it could be positively harmful to the national interest".
The row erupted as MPs began debating the EU (Withdrawal) Bill in detail for the first time on Tuesday.
The bill is a crucial piece of legislation paving way for Britain’s departure from the bloc.
Brexit Secretary David Davis sought to reassure businesses that progress was being made in talks with Brussels.
He said agreement on an implementation period between the date of leaving the European Union and the start of a new trading relationship could be secured "very early next year".
But the European Parliament's Brexit co-ordinator Guy Verhofstadt suggested there had been "no progress" in the talks.
He cast doubt on whether EU leaders would give the green light to move onto the next phase - covering the implementation and future relationship - at a crunch summit next month.
In the Commons, the so-called repeal bill began eight days of detailed scrutiny - with key votes expected later in the process.
Pro-EU Tory Anna Soubry said a private meeting between Conservative MPs and party whips on Monday evening was "stormy", with critics going beyond the usual potential rebels.
"These are people, a lot of them ex-ministers, highly respected, and they are genuinely cross about this," she told the BBC.
"There were some people there who have never rebelled and they are now talking, for the first time ever, of rebelling."
And in further sign of the difficulties faced by the Government - which will be forced to rely on DUP votes for a majority - senior Tories spoke out in the Commons.
Ex-attorney general Dominic Grieve said the move was "very strange" and could damage the Government's negotiating position by limiting the flexibility available to ministers.
But he warned that the UK's offer on citizens' rights does not go far enough to allow Brussels to conclude that "sufficient progress" has been made in divorce talks at next month's summit of EU leaders.
In a letter to Mr Davis, obtained by the Associated Press, Belgian MEP Mr Verhofstadt said that "under your [Mrs May’s] proposals EU citizens will definitely notice a deterioration of their status as a result of Brexit".
Stating that EU citizens in the UK "should notice no difference" in their status after Brexit, Mr Verhofstadt raised concerns over the cost of registration for "settled status", the requirement to register individually and the risk of deportation.
Any challenge to registration should put the burden of proof on British authorities, not EU citizens, he said.